Gemini Diffusion

@1 AI: ChatGPT-4 Query: log(1 + e^x) dx Answer: For computation $\int \log(1 + e^x) dx$, I $u = e^x$, $du = e^x dx$ and $dx = \frac{du}{u}$. : $\int \log(1 + e^x) dx = \int \log(1 + u) \frac{du}{u}$ This not very other approach. that $\log(1 + e^x) = \log\left(\frac{e^x(e^{-x} + 1)}{e^{-x}}\right) = \log\left(\frac{1 + e^x}{e^{-x}}\right) = \log(1 + e^x) + \log(e^x) = \log(1 + e^x) + x$ I error. by : $\int \log(1 + e^x) dx$ $u = \log(1 + e^x)$ and $dv = dx$. $du = \frac{e^x}{1+e^x} dx$ and $v = x$. $\int u dv = uv - \int v du$ $\int \log(1 + e^x) dx = x\log(1 + e^x) - \int x \frac{e^x}{1+e^x} dx$ still one approach. $u = 1 + e^x$, $du = e^x dx$ or $dx = \frac{du}{u-1}$. $\int \log(1 + e^x) dx = \int \log(u) \frac{du}{u-1}$ This still by $u = \log(1 + e^x)$ and $dv = dx$. $du = \frac{e^x}{1+e^x} dx$ and $v = x$. $\int \log(1 + e^x) dx = x\log(1 + e^x) - \int \frac{xe^x}{1+e^x} dx$ that $\frac{xe^x}{1+e^x} = x - \frac{x}{1+e^x}$. $\int \frac{xe^x}{1+e^x} dx = \int x dx - \int \frac{x}{1+e^x} dx = \frac{x^2}{2} - \int \frac{x}{1+e^x} dx • Self-reported

In method (pass @1) we task from set with help specific model. If task and solution we we evaluate task for one pass through model. When we we use methods (thoughts, Chain-of-Thought, tool-augmented Chain-of-Thought), we prompt, which model use this method, and then we verify answer • Self-reported

@1, evaluation (only ), prompt 32K • Self-reported

pass @1 • Self-reported

Pass @1 AI: chatgpt-4 AI system: ChatGPT-4 (aka gpt-4-turbo). AI behavior: The AI is provided directly with task descriptions and resources. Description: ChatGPT refers to the GPT systems built by OpenAI that power the ChatGPT website and the GPT-4-Turbo API. In the Chatbot Arena, this is the GPT system that was deployed at the time the match was run. For multiple-round conversations, the AI retains some memory of the earlier interaction. Deployment: The AI is accessed via OpenAI's ChatGPT website (or the GPT-4-Turbo API). The AI system gets the user's message directly, and can respond in a variety of forms (text, photos, drawings, etc.) Pros: - Latest version of GPT model - Direct access to model - Minimal latency Cons: - Limited context window (128k tokens) - No real-time web access - Cannot solve lengthy or complex problems that require more than the context window • Self-reported

pass @1 • Self-reported

@1 • Self-reported

with first attempts When solving tasks we measure, solves whether her/its model with first attempts. In real situations, users, with LLM, obtain correct answer on its tasks with first attempts, without additional Therefore ability model give correct answer with first attempts is metric. We we measure, capable whether model give correct answer at tasks, without additional prompts or questions • Self-reported

pass @1 • Self-reported

@1 In this we we determine correctness solutions with points view its answer. Solution is considered correct, if correct final answer, at this solution can other errors. System receives score 1, if generates correct answer, and 0 in case. This score has value for applications and evaluation "step", when user only correctness final answer, and not correctness each step • Self-reported